Hawking Radiation and the Hologram Theory

[PrestonFM]

According to Hawking Radiation, a black hole if left alone will eventually evaporate. As the black hole loses mass the area of the event horizon shrinks until both are gone.

The Hologram Theory says that as matter falls past the event horizon all the information pertaining to that matter is stored at the even horizon.

So here's my question, what happens to the information stored on the even horizon as the black hole evaporates. I presume that the Hawking Radiation carries it away, but I fail to see how there's a relationship between the radiation and the information stored.

My understanding of all this comes from watching Nova and reading Scientific American so I could be missing something basic. Thanks in advance!

 

[Naty1]

good issue statement..well done.

First a few clarifications:

According to Hawking Radiation, a black hole if left alone will eventually evaporate. As the black hole loses mass the area of the event horizon shrinks until both are gone.

The black hole only 'evaoprates', that is shrinks, when it is warmer than the surrounding universe...meantime until near the end of the universe when everything is really cold, most will continue to grow, swallowing just about anything..even each other. Also as far as is known there is no 'mass' really inside the black hole...no particles.

The Hologram Theory says that as matter falls past the event horizon all the information pertaining to that matter is stored at the even horizon.

and that includes the gravitational field, electromagnetic field, rotational momentum... those few 'hairs' [characteristics] we are able to observe. Actually the information is stored a a microscopic degree of freedom,a Planck length, outside the 'event horizon' at thge stretched horizon, made popular by Leonard Susskind.

... what happens to the information stored on the even horizon as the black hole evaporates. I presume that the Hawking Radiation carries it away, but I fail to see how there's a relationship between the radiation and the information stored.

In simple terms the information remains, but gets scrambled, so we can't really read it. Eventually, at the end of the universe when things get down close to absolute zero, it is all available but in a scrambled form.
The Hawking radiation can be intuitively described via virtual particles separating at the horizon; those with positive energy emerge...but I don't know of any mathematcial description for that other than the separate Unruh effect...what appears to be a good analogy.

One version of that 'scrambled' radiation from is Leonard Susskinds description in THE BLACK HOLE WAR, meaning his controversy with Stephin Hawking about whether information is lost...[a great non mathematical book, by the way] ...Hawking eventually conceded it is not lost.

...Events that a [free] falling observer reckons to be deep inside a black hole, another [outside, stationary] observer detects outside the horizon, scrambled among the Hawking radiation photons.

In fact, I believe an inertial [free falling] observer never sees any Hawking radiation which
is explained by the Unruh effect. You can read a fairly detailed description here:

http://en.wikipedia.org/wiki/Holographic_principle#Black_hole_information_paradox

Susskind expands much of what is in this section of Wikipedia into a whole book. In addition he describes string theory interpretations when strings for information at the stretched horizon and due to quantum vibrations break off...as Hawking radiation...

PS: Lots of this is still under study...here is one controversial paper...check the introduction and discussion for a sense of the issues.

 

[yuiop]

Also as far as is known there is no 'mass' really inside the black hole...no particles.

Hmmmmm ...

In fact, I believe an inertial [free falling] observer never sees any Hawking radiation ...

So let me see if I have this right. The observer falls through the event horizon (noticing nothing unusual) leaving a convenient holographic copy of his information at the horizon. As he falls and before he reaches the central singularity we assume the falling observer is still made of normal mass and still retains all his information. On arriving at the central singularity all the observers mass is converted into non-mass and all his information is converted into non-information (but the holograghic copy of his information at the EH is retained for future auditing purposes) ??

I guess it depends on what we mean by mass. Does mass mean particles, or does it mean localised energy that has an identifiable centre of momentum rest frame and has all the properties of momentum and active and passive gravitational qualities that we normally associate with mass?

For example if we play snooker with solar mass black holes, they certainly behave as if they has a mass equivalent to the Sun when they collide and they have a gravitational field equivalent to what we would expect a mass of that size to have and a black body temperature equivalent to what (relativistic) thermodynamic equations predict for a mass of that size and yet we say they have no mass?

 

[Naty1]

I can make a list of questions I don't understand either...this is not 'settled science' to use a silly and popular buzzword. There seem to be missing mathematical underpinnings...

As he falls and before he reaches the central singularity we assume the falling observer is still made of normal mass and still retains all his information.

One thing I have never figured out is why a free falling [inertial in GR] observer never sees a horizon on one hand [since there is no horizon] and yet apparently is 'exposed' to the singularity...that seems to thwart the 'nature abhors a naked singularity' postulate...It's likely explained via different reference frames but I've never seen such an explanation.

On arriving at the central singularity all the observers mass is converted into non-mass and all his information is converted into non-information (but the holograghic copy of his information at the EH is retained for future auditing purposes) ??

That's one thing I am sure about: nobody knows and what happens there divergence of QM and SR is one of the great issues in physics today...apparently it is thought tidal gravity gradually rips particles apart as they fall inside the horizon and move towards the singularity...all in finite time...

Another crazy thing is that from a classical GR description, it 'makes no difference' what is inside because in a sense it is causally cut off from outside the horizon...that's what a horizon is.

For a good discussion on just the gravitational and EM field outside a black hole, and how difficult it it to figure out just what is there, [and where does it come from] check the last several pages of this current discussion:

https://www.physicsforums.com/showthread.php?t=576698&page=6

post # 89

from Ryder

We cannot, then, identify a place or places, where where the gravitational field exists and carries energy, since whether the field carries energy also depends on the frame of reference. Gravitational energy is not localisable.

George Jones:
This means that gravitation energy cannot be included in the stress-energy-tensor field, as this is a mapping from spacetime into the space of tensors.

post #95:quote from PeterDonis

...That means extra terms come in due to the connection coefficients, and in certain special cases the extra terms have a simple interpretation in terms of "gravitational energy" being exchanged with ordinary matter-energy...

post#96
From Penrose:

Gravitational energy is a genuinely non-local entity. This does not imply there is no mathematical description of gravitational energy, however. Although I believe it is fair to say we do yet yet have a complete understanding of gravitational mass/energy, there is an important class of situations in which a very complete answer can be given.

 

[PeterDonis]

The observer falls through the event horizon (noticing nothing unusual) leaving a convenient holographic copy of his information at the horizon. As he falls and before he reaches the central singularity we assume the falling observer is still made of normal mass and still retains all his information. On arriving at the central singularity all the observers mass is converted into non-mass and all his information is converted into non-information (but the holograghic copy of his information at the EH is retained for future auditing purposes) ??

This is a key point that makes me wonder about the picture Susskind presents. The quantum "no cloning" theorem would seem to preclude having a second "auditing" copy of the infalling observer's information at the horizon, yet that's what Susskind seems to be saying is happening. (And btw, the "no cloning" theorem is really just another way of stating the principle that "quantum information is conserved", which is a key principle in Susskind's whole argument--for example, in the dispute with Hawking.)

I guess it depends on what we mean by mass. Does mass mean particles, or does it mean localised energy that has an identifiable centre of momentum rest frame and has all the properties of momentum and active and passive gravitational qualities that we normally associate with mass?

As Naty1 mentioned, we just had a long thread about this:

https://www.physicsforums.com/showthread.php?t=576698

Quick summary: "mass" can mean different things. For this discussion here, IMO, it's better to focus on "information", in other words, the microscopic quantum states of which the infalling observer (and everything else, including spacetime itself according to quantum gravity) is composed.

For example if we play snooker with solar mass black holes

You can't because black holes don't bounce off each other; they would merge. BH's may have "mass", but that doesn't mean they're snooker balls. However, as I said, I don't think this issue is really relevant to the questions we're raising about the holographic principle.

One thing I have never figured out is why a free falling [inertial in GR] observer never sees a horizon on one hand [since there is no horizon]

There is still a horizon, even to a freely falling observer; the horizon is a global feature of the spacetime and is there for all observers. The freely falling observer can't tell, from local observations, when he has crossed the horizon, but the horizon is still there.

and yet apparently is 'exposed' to the singularity...that seems to thwart the 'nature abhors a naked singularity' postulate...It's likely explained via different reference frames but I've never seen such an explanation.

No, the singularity is also a global feature of the spacetime and is there for all observers (or at least all observers who fall inside the horizon). But strictly speaking, the singularity is not actually part of the spacetime; it is a sign that "classical" (i.e., non-quantum) GR breaks down when the curvature gets too large, and a new theory is needed to describe the physics, presumably some theory of quantum gravity. (The best estimate of what "too large" means right now is basically that the "radius of curvature" locally is of the same order of magnitude as the Planck length, 10^-35 m. Any actual observer would have been destroyed by tidal gravity long before this point, of course.) What is a "global feature of the spacetime" is the Planck-sized "world tube" that marks off the point where the curvature reaches this scale.

 

[Naty1]

PeterDonis:

The quantum "no cloning" theorem would seem to preclude having a second "auditing" copy of the infalling observer's information at the horizon, yet that's what Susskind seems to be saying is happening.

I think this picture is analogous to the one you describe above in response to my comments:

There is still a horizon, even to a freely falling observer; the horizon is a global feature of the spacetime and is there for all observers.

It seems Susskind might say: there is no copy because the 'stuff' inside the horizon is not observable to us. In terms of the holographic principle, he'd probably say something like: quantum mechanics finds the location of information only slightly uncertain...the holographioc principle always locates the hologram out at the next level of observation...it makes it very uncertain!Whatever is inside, in some volume enclosed by a theoretical mathematical boundary, is the same as can be packed on the two dimensional area of the boundary.

That answer, and it is my interpretation rather his actual words, is as crazy as your answer above to me! [LOL]